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SEMISIMPLICITY OF HECKE AND (WALLED) BRAUER ALGEBRAS

  • HENNING HAAHR ANDERSEN (a1), CATHARINA STROPPEL (a2) and DANIEL TUBBENHAUER (a3)

Abstract

We show how to use Jantzen’s sum formula for Weyl modules to prove semisimplicity criteria for endomorphism algebras of $\mathbf{U}_{q}$ -tilting modules (for any field $\mathbb{K}$ and any parameter $q\in \mathbb{K}-\{0,-1\}$ ). As an application, we recover the semisimplicity criteria for the Hecke algebras of types $\mathbf{A}$ and $\mathbf{B}$ , the walled Brauer algebras and the Brauer algebras from our more general approach.

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Elements of the text in the article appear in colour online available at 10.1017/S1446788716000392.

H.H.A. was supported by the Center of Excellence grant ‘Centre for Quantum Geometry of Moduli Spaces (QGM)’ from the Danish National Research Foundation (DNRF), C.S. by a Hirzebruch professorship of the Max-Planck-Gesellschaft and D.T. by a research funding of the Deutsche Forschungsgemeinschaft (DFG) during this work.

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SEMISIMPLICITY OF HECKE AND (WALLED) BRAUER ALGEBRAS

  • HENNING HAAHR ANDERSEN (a1), CATHARINA STROPPEL (a2) and DANIEL TUBBENHAUER (a3)

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